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Cubic autocatalysis-based activation energy and thermophoretic diffusion effects of steady micro-polar nano-fluid

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Abstract

Cubic catalysts are very crucial in the fluid mechanics due to the chemical processes boosted with less energy. Cubic catalysts in the chemical process have numerous applications in the chemical engineering and food industry, like transformation or storage of different types of food materials, turning raw materials into useful products and accelerate the rate of food formation processes. This article brings the numerical analysis of the activation energy along with the impacts of the chemical process using the micro-polar nano-fluid subject to the cubic autocatalysis. Furthermore, thermophoretic diffusion and Brownian motion have also been investigated in this work. The set of equations of motion, temperature, concentration, and angular momentum in the differential form along with the associated boundary conditions has been presented for micro-polar nano-fluid. The similarity variables are being utilized for the conversion of ordinary differential equations (ODEs) into the partial differential equations (PDEs). A familiar shooting technique is applied to convert the boundary conditions into the initial value problems and further the first kind of obtained ODEs numerically handled by the bvp4c procedure. Moreover, the physical parameters with the profiles of velocity, temperature and concentration along with the physical quantities of couple stress and local skin friction have been discussed.

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Abbreviations

\(K_{1}\) :

Coupling constant

S :

Constant fluid characteristic

\({\text{Ea}}\) :

Activation energy coefficient

K :

Thermal conductivity

\(\tau\) :

Ratio parameter

T :

Fluid temperature

C :

Fluid concentration

\(D_{{\text{B}}}\) :

Coefficient of \({\text{Nb}}\)

\(D_{{\text{T}}}\) :

Thermophoresis coefficient

\(T_{\infty }\) :

Infinite temperature

T w :

Temperature of the plate

\(G_{1}\) :

Micro rotation constant

\(\rho\) :

Fluid density

\(g_{1}\) :

Magnitude of the gravity

\(\alpha\) :

Thermal diffusivity

\(c_{{\text{p}}}\) :

Specific heat

\(w\) :

Constant

\(B_{{\text{A}}}\) :

Pre-exponential factor

\(G_{{\text{r}}}\) :

Grashof number

\(G_{{\text{c}}}\) :

Buoyancy ratio parameter

\(G\) :

Micro rotation parameter

\(\Pr\) :

Prandtl number

\({\text{Nb}}\) :

Brownian motion

\({\text{Nt}}\) :

Thermophoresis parameter

\({\text{Sc}}\) :

Schmidt number

\(\lambda^{A}\) :

Activation energy parameter

\({\text{Bi}}_{\theta }\) :

Thermal Biot number

\(\beta^{*}\) :

Thermal expansion coefficient

\(\beta^{**}\) :

Mass diffusion coefficient

\(\nu\) :

Kinematic viscosity

\(c_{{\text{f}}}\) :

Skin friction coefficient

\({\text{R}}_{ex}\) :

Local Reynold number

\(N_{{{\text{u}}x}}\) :

Nusselt number

\(m_{{\text{w}}}\) :

Couple stress

\({\text{Sh}}_{x}\) :

Sherwood number

\(\sigma\) :

Micro rotation component

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Acknowledgements

The first author thanks the Faculty of Sciences and Liberal Arts, Rajamangala University of Technology Isan, Thailand.

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Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, Faculty of Sciences and Liberal Arts, Rajamangala University of Technology Isan, Nakhon Ratchasima, 30000, Thailand

    Peerapongpat Singkibud

  2. Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan

    Zulqurnain Sabir

  3. Department of Mathematics and Statistics, King Faisal University, P.O. Box 400, Al Ahsa, 31982, Saudi Arabia

    Muneerah Al Nuwairan

  4. Department of Mathematics, Faculty of Engineering at Zagazig, Zagazig University, Zagazig, 13512, Egypt

    R. Sadat

  5. Faculty of Engineering and Technology, Future University, Cairo, Egypt

    Mohamed R. Ali

  6. Basic Engineering Mathematics Department, Benha Faculty of Engineering, Benha University-Egypt, Banha, Egypt

    Mohamed R. Ali

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Singkibud, P., Sabir, Z., Al Nuwairan, M. et al. Cubic autocatalysis-based activation energy and thermophoretic diffusion effects of steady micro-polar nano-fluid. Microfluid Nanofluid 26, 50 (2022). https://doi.org/10.1007/s10404-022-02554-y

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